Problem: Subtract the following rational expressions. $\dfrac{9x^2+3}{14x^2-9}-\dfrac{-3x^2+11}{14x^2-9}=$
Solution: We want to subtract two rational expressions whose denominators are equal. We can do this by subtracting the numerators and keeping the denominator the same. [Does this fit with how we subtract rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{9x^2+3}{14x^2-9}-\dfrac{-3x^2+11}{14x^2-9} \\\\ &=\dfrac{(9x^2+3)-(-3x^2+11)}{14x^2-9} \\\\ &=\dfrac{9x^2+3+3x^2-11}{14x^2-9} \\\\ &=\dfrac{12x^2-8}{14x^2-9} \end{aligned}$ In conclusion, $\dfrac{9x^2+3}{14x^2-9}-\dfrac{-3x^2+11}{14x^2-9}=\dfrac{12x^2-8}{14x^2-9}$